1) In journalism contexts, there's evidence that shows that reporting on suicides in detail can lead to an increase in copycat suicides.
2) The stigma against mental illness and discrimination against the disabled. To acknowledge that mentally ill people deserve fulfilling lives, and also deserve the chance to opt out, would mean that people would have to acknowledge what exactly makes a mentally ill person's life full of suffering.
People have an easy time seeing someone dying of terminal cancer, in obvious pain, and determining that it's unfair to force them to stick around. It's clear that they aren't able to live their best lives anymore, because their opportunities are few, they're in a ton of pain, and they are suffering through and through.
On the other hand, mentally ill people already have a hard time being seen. There are people who insist we do not exist, or people who claim that there is no such thing as mental illness, just weak will. This hurts us more, because we don't get treated that way. People acknowledge that there are people who behave erratically, who are extremely difficult to talk to, who are impulsive and unstable, who are delusional and paranoid -- they will treat those individuals poorly, ignore them, fire them from their jobs, or refuse to hire them.
Because of the willful ignorance -- and maybe deep down, some genuine shame about the state of disability rights and mental illness awareness in this world -- people don't want to acknowledge that suicide is a natural, reasonable reaction to insurmountable pain and suffering.